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1
Preheat your oven to 350 F. Heat about a tablespoon of olive oil in a 12-inch cast iron skillet or oven-safe non-stick skillet over medium-high. Slice onions into thin strips and place them into the skillet, along with a sprinkle of salt. If your pan gets too crowded before you've added all the onions, let them cook down a bit before adding more. Once all your onions are in the pan, turn the heat down to medium low and let them cook, stirring occasionally until caramelized, about 15-20 minutes.
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2
Meanwhile, slice your parsnips into thin circle or semi-circles. Set these aside until your onions are a caramelized. Then, add your parsnips and bit more salt to the pan. Let the parsnips cook with the onions until tender, about 10 minutes. If your skillet gets a little too dry, add a little broth, water or white wine to deglaze. Once your parsnips are cooked through, turn off the heat, remove the vegetables from the pan and set aside.
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3
Whisk together your eggs, milk, cheese, thyme, about 1/2 teaspoon salt, and pepper to taste. Add your vegetables to the egg mixture and stir.
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4
Place your skillet back over medium heat with about a tablespoon of olive oil. Once the pan is hot, pour your egg mixture into the skillet, using a spatula to gently scrape the cooked egg off the bottom of the pan. Do this for about 2 minutes and then transfer your skillet to the oven. Bake for about 12-18 minutes, or until it jiggles just slightly in the middle when shaken. Serve immediately.
